Theoretical [1]}, [2]}, [3]}, [4]} and experimental [5]} studies have shown that thermal Hall conductance can change sign as temperature or magnetic field is varied. In Fig. REF c and Fig. REF d, we show the sign evolution of angular momentum together with the variation of thermal Hall conductance with temperature. See Methods and Supplementary Information for details on how these plots were obtained. The shape change of the boundary implies that previously identified positive zones have now been converted into negative areas (the blue color comes orange). We can see from Fig. REF c and Fig. REF d that there is a pinch point at around 60 mK where the transition happens. Currently, several competing theoretical proposals have attempted to explain the thermal Hall sign change behavior. The theoretical constructs range from the high temperature limiting value of thermal conductance to the Chern number of bands [2]}, propagation direction of edge modes [1]}, non-uniform Berry curvature over the Brillouin zone [3]}, and sensitivity of weight function in the thermal Hall formula [3]}. The importance of the weight function is manifested in the sign change behavior of Nernst conductivity [10]}. Irrespective of the conceptual reason for sign variation, we show that a measurable EdH mechanism can be observed in a host of frustrated lattices.
